Consider the linear function f(x)=mx+b, where m ≠0, on the interval [3,7]. Explain why the maximum value of the function over this interval must occur at one of the endpoints of the interval. Please Explain it’ll be greatly appreciated

  the function is either increasing or decreasing

Step-by-step explanation:

For m ≠ 0, the function must be either increasing or decreasing. If the function is increasing, it will have its maximum value at the right end of the interval. If it is decreasing, its maximum value will be at the left end of the interval.

up

step-by-step explanation:

the orientation of the parabolas can easily be found by analysing the power of x and y and their signs. if x is squared , parabola opens up and also if its coefficient is negative it opens down. if y is squared , the parabola opens right and also if its coefficient is negative it opens left. however in order to do the above analysis our equation must be in standard form .

our parabola is

which is not standard form of any parabola . hence we square on both hand side and convert it into standard form.

hence we see that x is squared and its coefficient is non negative . there for it opens up.

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step-by-step explanation: